Question

find the number of terms in an AP given that its first and last terms are 13 and - 23 respectively and that its common difference is -2 1/4​

Answer 1

Answer:

There are 17 terms in the sequence

Step-by-step explanation:

Arithmetic Sequence

An arithmetic sequence is a list of numbers with a definite pattern by which each term is calculated by adding or subtracting a constant number called common difference to the previous term. If n is the number of the term, then:

$a_n=a_1+(n-1)r$

Where an is the nth term, a1 is the first term, and r is the common difference.

In the problem at hand, we are given the first term a1=13, the last term an=-23, and the common difference r=-2 1/4. Let's solve the equation for n:

$\displaystyle n=1+\frac{a_n-a_1}{r}$

We need to express r as an improper or proper fraction:

$\displaystyle r=-2\frac{1}{4}=-2-\frac{1}{4}=-\frac{9}{4}$

Substituting:

$\displaystyle n=1+\frac{-23-13}{-\frac{9}{4}}$

$\displaystyle n=1+\frac{-36}{-\frac{9}{4}}$

$\displaystyle n=1+36*\frac{4}{9}=17$

n=17

There are 17 terms in the sequence